A System to Test for Convergence of the Gibbs Sampler
Angelo J. Canty
Department of Statistics
University of Toronto
Ph.D. thesis defended April 10, 1995.
Abstract
A computational technique which has gained a lot of popularity in the
Bayesian community in recent years is that of Markov Chain Monte Carlo
methods. The Gibbs Sampler is among the most widely used of these methods
due, in a large part, to
its simplicity. One of the major problems with this and many other forms
of MCMC is in knowing when enough iterations have been completed for us to
be confident in the accuracy of Monte Carlo inferences on the
output of the algorithm. Many
attempts at answering this question have been proposed in the last few years
and in this thesis I shall look at some of these methods. I
shall also propose a new diagnostic which performs very well in examples.
These examples include models which are known to exhibit slow convergence and
characteristics that cause problems for
many existing convergence diagnostics.
The new diagnostic has the advantage of being determined quantitatively
and so the task of deciding whether the Markov chains have reached their
stationary state or not can be made more automatic.
This page is maintained by Angelo Canty,
cantya@mcmaster.ca
Last updated on July 23, 2001